The increasing spread of mobile communication has led to a steady evolution of communication technology, including the Global System for Mobile Communications (GSM), its evolution EDGE, the Universal Mobile Telecommunications System (UMTS) and the Long Term Evolution (LTE), which are also referred to as different generations of mobile cellular technology. There is also progress in the implementation within existing generations of mobile cellular technology such GSM. On a worldwide perspective, the GSM network is still the most popular cellular mobile communication system having billions of subscribers, which success often leads to shortage in network capacity.
Network capacity may generally be increased using closely spaced cells to serve the increasing number of mobile devices. However, closely spaced cells increase co-channel interference. Network operators prefer reusing their allocated frequency spectrum and existing infrastructure, which is why Single Antenna Interference Cancellation (SAIC) and Downlink Advance Receiver Performance (DARP-I) have been implemented on the side of the mobile devices in order to maximize the reuse of the twelve frequencies available for a base station in GSM networks. Such improvements avoid additional antennas, and mitigate the co-channel interference and adjacent channel interference for mobile devices in GSM and Enhanced Data Rate for GSM Evolution (EDGE) networks.
Another improvement compatible with both existing GSM networks and existing mobile devices is the so-called Voice Services over Adaptive Multi-User Orthogonal Sub-Channels (VAMOS), which pairs two mobile devices on the same channel. However, this pairing further increases the interference level and thus requires a better interference mitigation capability of the GSM receiver. Network capacity can also be limited by interference in any other mobile communication generation, including LTE.
WO 2006/136875 A1 describes a filter for “whitening” noise, which is referred to as Spatio-Temporal Interference Rejection Combining (ST-IRC), to suppress interference and noise during synchronization and channel estimation in GSM and EDGE networks. According to ST-IRC, the receiver “whitens” the noise spatially and temporally by means of a “whitening” filter. The “colored” interference or noise is “whitened” across spatial and temporal branches leading to improved receiver performance.
The whitening filter has to be generated individually depending on the current correlation of the noise across the received branches. This requires a so-called inverse Cholesky decomposition, as outlined in what follows.
Denoting the amplitudes of the “colored” noise on the multiple branches by u1, . . . , the colored noise is collectively referred to using a vector U=(u1, . . . )T. The colored noise U is a stochastic vector. Denoting the expectation value, i.e., the “averaging”, of the stochastic process by E, a noise covariance matrix of the colored noise U isΛ=E[UUH].
The whitening filter is a linear transformation, F, that yields “whitened” noise W when applied to the “colored” noise U, as symbolized byW=FU. 
“White” noise means that the transformed signal including the “white” noise W has a noise covariance that is equal to the identity matrix (up to an over-all normalization factor):E[WWH]=E[FU(FU)H]=I, wherein the matrix F representing the “whitening” filter is deterministic, so that it can be factored out of the expectation value resulting inFΛFH=I.  (1)
Since the noise covariance matrix  is by definition a Hermitian and positive-definite matrix, it can be subject to a Cholesky factorization,Λ=LLH,wherein the lower triangular matrix of the Cholesky decomposition is denoted by L=Chol (). One solution for the filter F in Eq. (1) is given by:F=L−1=[Chol(Λ)]−1.  (2)
The generation of the filter F thus requires the computation of an inverse Cholesky decomposition. As a consequence of realistic channel profiles, including those specified by the 3rd Generation Partnership Project (3GPP), the covariance matrix , based on which the filter F is computed, is often ill-conditioned. The covariance matrix sometimes comes close to singular or even yields technically meaningless results. This leads to a significant degradation of the receiver performance, e.g., when the generation of the filter is implemented on a fixed-point processor. Ill-conditioned matrices particularly occur in the so-called block Cholesky decomposition, which is frequently implemented in existing receivers and described in the review article “Block Cholesky Algorithms” by P. A. Steeves, Geodetic Software Systems.